How to follow dynamic paint brush direction with object in Blender V2.80 beta and 2.79b?
Well, looks like nobody could help me with this one. I managed to come up with a solution for this but with a bit different method. It works in both Blender V2.79b and V2.80 Beta. I added a path to make nicer turns but finally the turns are happening.
The following was setup, additionally, to get an object to follow the waveform of the ocean while it moves around the surface:


A path was added - in this case a BezierCircle in the Outliner called 'BezierCircle - Path to follow' and animated.
Added a Plane and subdivided it 2 times in Edit mode. 'Called Plane on water surface' on the image below. Added a Shrinkwrap modifier to it and set the target to be the 'Ocean', that mowed the plane to the ocean surface. Added an Object Constraint and the target was the 'BezierCircle - Path to follow' object. Ticked the Follow Curve
The 'Boat -constrained to Plane on water surface' object added a Copy Location and a Copy Rotation constrains. Both have the target set to 'Plane on water surface' object and it Vertex Group selected to 'Group' that was defined for that plane.




The purple plane on the bellow image is the 'Plane on water surface' object that follows the waves with the Shrinkwrap modifier and the boat is constrained to it with Location and Rotation. The orange path is the one the 'Plane on water surface' object follows.

 

This is a tight turn but demonstrates that the turning direction is followed.



The same section of the path but with material applied. This is not baked or animated yet, only played.